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st: RE: Positive log likelihood values in a switching regression


From   Zhong Liu <zl1969@googlemail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Positive log likelihood values in a switching regression
Date   Fri, 14 Sep 2007 13:04:34 -0400

Hi, Anil:

I got the same concern but I have found an answer in the STATA official
website. See:

http://www.stata.com/support/faqs/stat/wbl.html

Regards,Zhong

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Anil Caliskan
Sent: 14 September 2007 12:33
To: statalist@hsphsun2.harvard.edu
Subject: st: Positive log likelihood values in a switching regression

Dear Stata list:

I am trying to determine a regime switch date using the framework suggested
in Goldfeld and Quandt (1973) and applied in Mankiw (1987). The regressions
are modeled as below: 

yt = beta01 + beta11*x1t + beta21*t + beta31*t^2 + e1t for t=1,...,i-1
yt = beta02 + beta12*x1t + beta22*t + beta32*t^2 + e2t for t=i,...,N

I ran the regressions for all possible regime switch dates, i's, and
calculated the log likelihood based on the formula:

logL=-0.5*N*log(2*pi)-(i-1)*log(sigma1^2)-(N-(i-1))*log(sigma2^2)-0.5*(e1'e1
/sigma1^2)-0.5*(e2'e2/sigma2^2)

I obtained e.'e. by using e(rss) and sigma. by using e(rmse) after each
regression. 

The likelihood function that I computed is concave, however values are
positive, which is the cause of my concern. I would be grateful if you help
me understand why I am getting positive instead of negative values and if I
am making a mistake.

Thanks in advance.

Anil Caliskan. 



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